Thermal spiral inductor using 3D printed shape memory kirigami

Spiral inductors are required to realise high inductance in radio frequency (RF) circuits. Although their fabrication by using micro-electrical–mechanical systems, thin films, actuators, etc., has received considerable research attention, current approaches are both complex and expensive. In this study, we designed and fabricated a thermal spiral inductor by using a three-dimensional (3D) printed shape-memory polymer (SMP). The proposed inductor was inspired by kirigami geometry whereby a two-dimensional (2D) planar geometric shape could be transformed into a 3D spiral one to change the inductance by heating and manually transform. Mechanical and electromagnetic analyses of the spiral inductor design was conducted. Hence, in contrast with the current processes used to manufacture spiral inductors, ours can be realised via a single facile fabrication step.

www.nature.com/scientificreports/ 10 6 S/m was used for the conductive layer in the spiral inductor 19 . In general, the shape of an item fabricated with SMP formed by applying external heat and using external force will reacquire its shape after cooling. The transforming and restoring temperatures are determined by using the glass-transition temperature ( T g ), which is the temperature transition point between the rigid glassy and soft rubbery states. Figure 1a shows the four steps comprising the thermally transformed SMP filament shape recovery cycle.
1. The original 3D-printed structure is transformed when T > T g .
2. An external force is then applied to transform the structure while heating. 3. The external force is continuously applied to retain the new shape as the heat is reduced to room temperature and is then removed while the new shape remains in place. 4. Reapplying external heat ( T > T g ) restores the new shape to the original shape. Figure 1b shows elastic modulus changes depending on the applied temperature of the SMP material; it can be seen that the elastic modulus value decreases as the temperature was increased from approximately 35 to 75 °C. In this work, we used SMP filaments with a T g of 55 °C and a measured density of 1073.596 kg/m 3 . The SMP is in the glassy state when the external temperature is lower than the room temperature and in the rubbery state when the external temperature is higher than 80 °C. The SMP has an elastic modulus value of 10 9 Pa in the glassy state (i.e., it is still a hard solid) and an elastic modulus of 10 6 Pa in the rubbery state (i.e., it is flexibly transformable) 20,21 .
We employed the additive-manufacturing method FDM 3D-printing to build the melting filament layer by layer in the desired geometry. Figure 1c shows the manufacturing process to fabricate the proposed SMPbased spiral inductor. The heated nozzle melted the SMP filament and extruded it layer by layer. In addition, the attached filament layer was cooled by using a fan and became hard. Silver paste was applied to the top and bottom surfaces using a brush to provide its electrical characteristics. Figure 2 shows images of the fabricated sample in the original and transformed shapes from various viewpoints. The planar spiral line areas were transformed into a conical shape. The fabricated sample was transformed by hand and heat was applied using a hot plate. An SMA connector was used to measure the inductance of the device.
Investigation of the 3D-printed thermal spiral inductor. In general, a spiral inductor is fabricated with a via or vertical shape air bridge. However, the FDM method has a manufacturing limitation when fabricating a horizontal structure in air as the structure needs to be supported. Thus, we designed an inclined air bridge, the angle of which was determined via fabrication experiments. Figure 3 shows details of the design parameters of the fabricated sample in the original and transformed shapes. Figure 3a shows the design parameters for the original 2D planar rectangular shape of the proposed inductor. The performance of a spiral inductor is determined by the number of turns in, as well as the inner and outer diameter of the spiral range. The designed inductor is surrounded by a square grid that has two functions: as the ground and as a fixed frame. The inductor is surrounded by a microstrip line with an input impedance of around 70 Ω. The inclined air bridge fabrication also affects the inductor width. The air bridge design parameters were determined for a single-step fabrication process without any post-processing. The air bridge has height h = 6 mm, an angle from the horizontal of 55 • and a total length of 16.1 mm. In addition, the distance between the lines is 0.3 mm and the internal diameter ( D in ) and external diameter ( D out ) of the inductor are 2.9 and where N is the number of turns in the spiral inductor, When heat is applied to the spiral planar inductor and force is applied perpendicular to the air bridge plane, then the parameters change, as shown in Fig. 3b. The transformed shape is similar to a quadrangular pyramid. The total height s a = 12.5 mm; the distances between the inductor lines s 1 , s 2 and s 3 = 3.5, 4.5 and 0.5 mm, respectively; and angle of transformation α = 30°. The inductance of the transformed inductor can be approximated to that of a conical inductor as follows: where α is the angle of a conical inductor and L cy is the inductance of a cylindrical inductor with has same radius size determined as In addition, the Q-factor of the inductor can be expressed as where f is the frequency, L is the inductance and R is the resistance 22,23 .
We used Ansys high-frequency structure simulator (HFSS) to investigate the fabricated kirigami-inspired structure operating as a spiral inductor with silver paste conductivity. Figure 3c shows that the simulated inductance by the transformed and restored shapes in the 250 MHz range increased from 95 to 102.7 nH, respectively, and that the self-resonant frequency decreased from 637 to 578 MHz, respectively. Figure 3d shows that the maximum Q-factor decreased from 102.6 to 94.5, respectively. Deforming the structure caused the mutual inductance and capacitance between the inductor lines to decrease, which affected the resonant frequency and Q-factor [24][25][26] .
We also simulated the transformed shape to investigate its physical characteristics by using a general constitutive SMP based on SMP materials used in various constitutive models and mechanical applications such as actuators. We used COMSOL Multiphysics software to simulate the mechanical transformation properties for the proposed 3D-printed spiral inductor in which the partial differential equations are used to simulate the physical phenomena. The spiral inductor structure in HFSS was extracted and imported to COMSOL Multiphysics and subsequently analysed. We used Young's modulus, which depends on three distinct states based on the temperature: glassy (T < T g ), glass-transition (T g ) and rubbery (T > T g ). The SMP used in this work had a Young's modulus value of 1 MPa, a Poisson's ratio of 0.4 and a density of 1073.596 kg/m 3 . The prepared SMP filament had an approximately linearly decreasing elastic modulus with increasing temperature in the glass-transition region. The fabricated structure transformed at 75 °C under a force applied by hand in the perpendicular direction to the (1) L pl = µN 2 r avg ln 2.46 R r + 0.2R r , (2) L co = L 2 pl cos 2 (α) + L 2 cy sin 2 (α), www.nature.com/scientificreports/ air bridge, which closed the surrounding line plane. The COMSOL Multiphysics program was used to simulate total displacement under the applied stress at 75 °C and SMP elastic modulus E = 10 6 . Figure 3e,f show the simulation results for the inductor in the transformed shape: a total displacement of 12.5 mm occurred under a load of 0.03 N perpendicular to the air bridge. In addition, the maximum applied stress of 1.6 × 10 5 Pa was concentrated at the base of the air bridge. Figure 4 shows the measurement results of the characteristics of the fabricated thermal inductor using a vector network analyser (VNA). The results in Fig. 4a show that when considering the surface resistance, the measured inductance results were the same as the simulation results. As the transformed inductor was restored to the original 2D planar spiral inductor shape in the 250 MHz range, the average inductance changed from 117.3 to 140.9 nH (20.12%), respectively. Moreover, the self-resonant frequency decreased from 600 to 528 MHz,  2 mm); h, the height of the air bridge (6 mm); w, the width of the inductor spiral (1.4 mm); g, the width of the surrounding square grid (2.3 mm); S a , the height of the spiral (12.5 mm); S 1 -S 3 , the distances between the inductor lines in the spiral (3.5, 4.5 and 0.5 mm, respectively); a, the angle of transformation (30°). www.nature.com/scientificreports/ respectively. Figure 4b shows the measured maximum Q-factor increased from 1.73 to 2.52, respectively. In the measurement in Fig. 4b, we notice that the Q-factor is lower compared to the simulated result in Fig. 3d. This is due to the low conductivity of silver ink used in the fabrication. We found that the conductivity of this silver ink is approximately 15,000 S/m as compared between simulation and measurement in Fig. 4b. Figure 4c shows measured results of the thermal spiral inductor after 5 times repeating cycles. We notice that the inductance values of the sample is almost stable with a minor deviation. Although the simulated inductor is the same size as the fabricated sample, applying the silver past to the rough surface caused by using the FDM method reduced the surface conductivity. The angle of the transformed shape affected the Q-factor and parameters s 1 , s 2 and s 3 (1.5, 5 and 2 mm, respectively). The experimental results indicate that the SMP material used in the 3D-printed structure can be applied to electromagnetic structures and sensor devices.

Conclusions
We fabricated a novel SMP-based thermal spiral inductor fabricated by using FDM 3D-printing technology. Silver paste was applied to the top and bottom surfaces to provide the electrical characteristics of the proposed spiral inductor. The SMP-based thermal spiral inductor could be transformed by applying a force at 75 °C and returned to its original shape after cooling to room temperature. The fabricated inductor in both the original and transformed shapes had different inductances, Q-factor values and self-resonant frequencies. Restoring the original shape from the transformed shape increased the Q-factor and reduced the self-resonant frequency and inductance (the latter by 20.12%).

Methods
Fabrication and measurement of the 3D-printed inductor. The designed kirigami-inspired 3D structure was printed by using a 3DWOX 7X 3D printer. The SMP filament was purchased from SMP Technologies Inc. The nozzle and bed temperatures to achieve a clear sample were 210 and 100 °C, respectively, and the infill affecting the density was 20%. We coated ELCOAT P-100 silver paste with a bulk conductivity of 10 6 S/m used as conductivity ink on the top and bottom planes by using a brush, which was allowed to dry to room temperature (25 °C) for 12 h. The resistance measured by using a multimeter was 1 Ω. In the next step, conductive epoxy CW 2400 was used to connect the fabricated inductor with the SMA connector because the SMP material distorts and melts at high temperatures. The 3D-printer had manufacturing errors in the x-, y-and z-directions, with average differences (fabricated sample size vs. designed sample size) of + 0.2 mm, + 0.1 mm and − 0.15 mm, respectively, which were compensated for in the fabrication.
To determine the value of inductance (L) and quality factor (Q) in the measurement, we measure the scattering parameter (S-matrix) of the proposed spiral inductor using VNA and then convert to admittance matrix (Y-matrix). The values of L and Q are determined from the following equation 27 :

Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.